Question

प्रश्न 1 से 22 तक निम्नलिखित सीमाओं के मान प्राप्त कीजिए : $\lim_{x\rightarrow0}\dfrac{\cos 2x - 1}{\cos x - 1}$

Answer 1

hope it is helpful to you

Answer 2

Answer:

Step-by-step explanation:

$\lim_{x\rightarrow0}\dfrac{\cos 2x - 1}{\cos x - 1}\\\\=\lim_{x\rightarrow0}\dfrac{(2 \cos ^2x-1)- 1}{\cos x - 1}\\\\=\lim_{x\rightarrow0}\dfrac{2(\cos ^2x-1)}{\cos x - 1}\\\\=\lim_{x\rightarrow0}2[\dfrac{(\cos x-1)(\cos x+1)}{\cos x - 1}\\\\=2\lim_{x\rightarrow0}(\cos x+1)}$

x →0 रखने पर  

= 2 (cos 0 + 1 )

= 2 ( 1 + 1 )

= 2 (2)

=4

अतः  $\lim_{x\rightarrow0}\dfrac{\cos 2x - 1}{\cos x - 1}$  का  मान  4 होगा।